Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A

Percentage Accurate: 84.6% → 90.5%

Time: 17.5s

Alternatives: 12

Speedup: 0.5×

Specification

Math

\[\begin{array}{l} \\ \frac{x - y \cdot z}{t - a \cdot z} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (/ (- x (* y z)) (- t (* a z))))

C

double code(double x, double y, double z, double t, double a) {
	return (x - (y * z)) / (t - (a * z));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = (x - (y * z)) / (t - (a * z))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return (x - (y * z)) / (t - (a * z));
}

Python

def code(x, y, z, t, a):
	return (x - (y * z)) / (t - (a * z))

Julia

function code(x, y, z, t, a)
	return Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(a * z)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = (x - (y * z)) / (t - (a * z));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(a * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 84.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y \cdot z}{t - a \cdot z} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (/ (- x (* y z)) (- t (* a z))))

C

double code(double x, double y, double z, double t, double a) {
	return (x - (y * z)) / (t - (a * z));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = (x - (y * z)) / (t - (a * z))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return (x - (y * z)) / (t - (a * z));
}

Python

def code(x, y, z, t, a):
	return (x - (y * z)) / (t - (a * z))

Julia

function code(x, y, z, t, a)
	return Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(a * z)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = (x - (y * z)) / (t - (a * z));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(a * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 90.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+56} \lor \neg \left(z \leq 3 \cdot 10^{+95}\right):\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.55e+56) (not (<= z 3e+95)))
   (/ y (- a (/ t z)))
   (/ (- x (* z y)) (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.55e+56) || !(z <= 3e+95)) {
		tmp = y / (a - (t / z));
	} else {
		tmp = (x - (z * y)) / (t - (z * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.55d+56)) .or. (.not. (z <= 3d+95))) then
        tmp = y / (a - (t / z))
    else
        tmp = (x - (z * y)) / (t - (z * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.55e+56) || !(z <= 3e+95)) {
		tmp = y / (a - (t / z));
	} else {
		tmp = (x - (z * y)) / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.55e+56) or not (z <= 3e+95):
		tmp = y / (a - (t / z))
	else:
		tmp = (x - (z * y)) / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.55e+56) || !(z <= 3e+95))
		tmp = Float64(y / Float64(a - Float64(t / z)));
	else
		tmp = Float64(Float64(x - Float64(z * y)) / Float64(t - Float64(z * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.55e+56) || ~((z <= 3e+95)))
		tmp = y / (a - (t / z));
	else
		tmp = (x - (z * y)) / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.55e+56], N[Not[LessEqual[z, 3e+95]], $MachinePrecision]], N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.55000000000000002e56 or 2.99999999999999991e95 < z

   1. Initial program 58.5%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 58.5%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 58.5%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 42.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{t - a \cdot z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 42.0%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(y \cdot z\right)}{t - a \cdot z}} \]

      2. mul-1-neg 42.0%

         \[\leadsto \frac{\color{blue}{-y \cdot z}}{t - a \cdot z} \]

      3. distribute-rgt-neg-out 42.0%

         \[\leadsto \frac{\color{blue}{y \cdot \left(-z\right)}}{t - a \cdot z} \]

      4. associate-/l* 55.7%

         \[\leadsto \color{blue}{\frac{y}{\frac{t - a \cdot z}{-z}}} \]

      5. *-commutative 55.7%

         \[\leadsto \frac{y}{\frac{t - \color{blue}{z \cdot a}}{-z}} \]

   7. Simplified 55.7%

      \[\leadsto \color{blue}{\frac{y}{\frac{t - z \cdot a}{-z}}} \]

   8. Taylor expanded in t around 0 80.4%

      \[\leadsto \frac{y}{\color{blue}{a + -1 \cdot \frac{t}{z}}} \]
   9. Step-by-step derivation

      1. mul-1-neg 80.4%

         \[\leadsto \frac{y}{a + \color{blue}{\left(-\frac{t}{z}\right)}} \]

      2. unsub-neg 80.4%

         \[\leadsto \frac{y}{\color{blue}{a - \frac{t}{z}}} \]

   10. Simplified 80.4%

       \[\leadsto \frac{y}{\color{blue}{a - \frac{t}{z}}} \]

   if -1.55000000000000002e56 < z < 2.99999999999999991e95

   1. Initial program 99.2%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+56} \lor \neg \left(z \leq 3 \cdot 10^{+95}\right):\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 72.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t - z \cdot a}\\ t_2 := \frac{y}{a - \frac{t}{z}}\\ \mathbf{if}\;z \leq -2 \cdot 10^{+22}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-138}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-77} \lor \neg \left(z \leq 9.2 \cdot 10^{+14}\right) \land z \leq 2.5 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (- t (* z a)))) (t_2 (/ y (- a (/ t z)))))
   (if (<= z -2e+22)
     t_2
     (if (<= z -6e-34)
       t_1
       (if (<= z -4.5e-138)
         (/ (- x (* z y)) t)
         (if (or (<= z 6.4e-77) (and (not (<= z 9.2e+14)) (<= z 2.5e+45)))
           t_1
           t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t - (z * a));
	double t_2 = y / (a - (t / z));
	double tmp;
	if (z <= -2e+22) {
		tmp = t_2;
	} else if (z <= -6e-34) {
		tmp = t_1;
	} else if (z <= -4.5e-138) {
		tmp = (x - (z * y)) / t;
	} else if ((z <= 6.4e-77) || (!(z <= 9.2e+14) && (z <= 2.5e+45))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (t - (z * a))
    t_2 = y / (a - (t / z))
    if (z <= (-2d+22)) then
        tmp = t_2
    else if (z <= (-6d-34)) then
        tmp = t_1
    else if (z <= (-4.5d-138)) then
        tmp = (x - (z * y)) / t
    else if ((z <= 6.4d-77) .or. (.not. (z <= 9.2d+14)) .and. (z <= 2.5d+45)) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t - (z * a));
	double t_2 = y / (a - (t / z));
	double tmp;
	if (z <= -2e+22) {
		tmp = t_2;
	} else if (z <= -6e-34) {
		tmp = t_1;
	} else if (z <= -4.5e-138) {
		tmp = (x - (z * y)) / t;
	} else if ((z <= 6.4e-77) || (!(z <= 9.2e+14) && (z <= 2.5e+45))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (t - (z * a))
	t_2 = y / (a - (t / z))
	tmp = 0
	if z <= -2e+22:
		tmp = t_2
	elif z <= -6e-34:
		tmp = t_1
	elif z <= -4.5e-138:
		tmp = (x - (z * y)) / t
	elif (z <= 6.4e-77) or (not (z <= 9.2e+14) and (z <= 2.5e+45)):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(t - Float64(z * a)))
	t_2 = Float64(y / Float64(a - Float64(t / z)))
	tmp = 0.0
	if (z <= -2e+22)
		tmp = t_2;
	elseif (z <= -6e-34)
		tmp = t_1;
	elseif (z <= -4.5e-138)
		tmp = Float64(Float64(x - Float64(z * y)) / t);
	elseif ((z <= 6.4e-77) || (!(z <= 9.2e+14) && (z <= 2.5e+45)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (t - (z * a));
	t_2 = y / (a - (t / z));
	tmp = 0.0;
	if (z <= -2e+22)
		tmp = t_2;
	elseif (z <= -6e-34)
		tmp = t_1;
	elseif (z <= -4.5e-138)
		tmp = (x - (z * y)) / t;
	elseif ((z <= 6.4e-77) || (~((z <= 9.2e+14)) && (z <= 2.5e+45)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e+22], t$95$2, If[LessEqual[z, -6e-34], t$95$1, If[LessEqual[z, -4.5e-138], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[Or[LessEqual[z, 6.4e-77], And[N[Not[LessEqual[z, 9.2e+14]], $MachinePrecision], LessEqual[z, 2.5e+45]]], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2e22 or 6.39999999999999999e-77 < z < 9.2e14 or 2.5e45 < z

   1. Initial program 67.6%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 67.6%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 67.6%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 48.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{t - a \cdot z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 48.7%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(y \cdot z\right)}{t - a \cdot z}} \]

      2. mul-1-neg 48.7%

         \[\leadsto \frac{\color{blue}{-y \cdot z}}{t - a \cdot z} \]

      3. distribute-rgt-neg-out 48.7%

         \[\leadsto \frac{\color{blue}{y \cdot \left(-z\right)}}{t - a \cdot z} \]

      4. associate-/l* 58.3%

         \[\leadsto \color{blue}{\frac{y}{\frac{t - a \cdot z}{-z}}} \]

      5. *-commutative 58.3%

         \[\leadsto \frac{y}{\frac{t - \color{blue}{z \cdot a}}{-z}} \]

   7. Simplified 58.3%

      \[\leadsto \color{blue}{\frac{y}{\frac{t - z \cdot a}{-z}}} \]

   8. Taylor expanded in t around 0 77.1%

      \[\leadsto \frac{y}{\color{blue}{a + -1 \cdot \frac{t}{z}}} \]
   9. Step-by-step derivation

      1. mul-1-neg 77.1%

         \[\leadsto \frac{y}{a + \color{blue}{\left(-\frac{t}{z}\right)}} \]

      2. unsub-neg 77.1%

         \[\leadsto \frac{y}{\color{blue}{a - \frac{t}{z}}} \]

   10. Simplified 77.1%

       \[\leadsto \frac{y}{\color{blue}{a - \frac{t}{z}}} \]

   if -2e22 < z < -6e-34 or -4.50000000000000008e-138 < z < 6.39999999999999999e-77 or 9.2e14 < z < 2.5e45

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 84.0%

      \[\leadsto \color{blue}{\frac{x}{t - a \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 84.0%

         \[\leadsto \frac{x}{t - \color{blue}{z \cdot a}} \]

   7. Simplified 84.0%

      \[\leadsto \color{blue}{\frac{x}{t - z \cdot a}} \]

   if -6e-34 < z < -4.50000000000000008e-138

   1. Initial program 99.9%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.9%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 77.6%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+22}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-34}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-138}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-77} \lor \neg \left(z \leq 9.2 \cdot 10^{+14}\right) \land z \leq 2.5 \cdot 10^{+45}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - z \cdot a\\ t_2 := \frac{x}{t\_1}\\ t_3 := \frac{y}{a - \frac{t}{z}}\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+22}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-34}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-134}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-76}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+19}:\\ \;\;\;\;\frac{y}{\frac{t\_1}{-z}}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+46}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* z a))) (t_2 (/ x t_1)) (t_3 (/ y (- a (/ t z)))))
   (if (<= z -1.55e+22)
     t_3
     (if (<= z -5e-34)
       t_2
       (if (<= z -1.4e-134)
         (/ (- x (* z y)) t)
         (if (<= z 1.4e-76)
           t_2
           (if (<= z 1.25e+19)
             (/ y (/ t_1 (- z)))
             (if (<= z 1.9e+46) t_2 t_3))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (z * a);
	double t_2 = x / t_1;
	double t_3 = y / (a - (t / z));
	double tmp;
	if (z <= -1.55e+22) {
		tmp = t_3;
	} else if (z <= -5e-34) {
		tmp = t_2;
	} else if (z <= -1.4e-134) {
		tmp = (x - (z * y)) / t;
	} else if (z <= 1.4e-76) {
		tmp = t_2;
	} else if (z <= 1.25e+19) {
		tmp = y / (t_1 / -z);
	} else if (z <= 1.9e+46) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t - (z * a)
    t_2 = x / t_1
    t_3 = y / (a - (t / z))
    if (z <= (-1.55d+22)) then
        tmp = t_3
    else if (z <= (-5d-34)) then
        tmp = t_2
    else if (z <= (-1.4d-134)) then
        tmp = (x - (z * y)) / t
    else if (z <= 1.4d-76) then
        tmp = t_2
    else if (z <= 1.25d+19) then
        tmp = y / (t_1 / -z)
    else if (z <= 1.9d+46) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (z * a);
	double t_2 = x / t_1;
	double t_3 = y / (a - (t / z));
	double tmp;
	if (z <= -1.55e+22) {
		tmp = t_3;
	} else if (z <= -5e-34) {
		tmp = t_2;
	} else if (z <= -1.4e-134) {
		tmp = (x - (z * y)) / t;
	} else if (z <= 1.4e-76) {
		tmp = t_2;
	} else if (z <= 1.25e+19) {
		tmp = y / (t_1 / -z);
	} else if (z <= 1.9e+46) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (z * a)
	t_2 = x / t_1
	t_3 = y / (a - (t / z))
	tmp = 0
	if z <= -1.55e+22:
		tmp = t_3
	elif z <= -5e-34:
		tmp = t_2
	elif z <= -1.4e-134:
		tmp = (x - (z * y)) / t
	elif z <= 1.4e-76:
		tmp = t_2
	elif z <= 1.25e+19:
		tmp = y / (t_1 / -z)
	elif z <= 1.9e+46:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(z * a))
	t_2 = Float64(x / t_1)
	t_3 = Float64(y / Float64(a - Float64(t / z)))
	tmp = 0.0
	if (z <= -1.55e+22)
		tmp = t_3;
	elseif (z <= -5e-34)
		tmp = t_2;
	elseif (z <= -1.4e-134)
		tmp = Float64(Float64(x - Float64(z * y)) / t);
	elseif (z <= 1.4e-76)
		tmp = t_2;
	elseif (z <= 1.25e+19)
		tmp = Float64(y / Float64(t_1 / Float64(-z)));
	elseif (z <= 1.9e+46)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (z * a);
	t_2 = x / t_1;
	t_3 = y / (a - (t / z));
	tmp = 0.0;
	if (z <= -1.55e+22)
		tmp = t_3;
	elseif (z <= -5e-34)
		tmp = t_2;
	elseif (z <= -1.4e-134)
		tmp = (x - (z * y)) / t;
	elseif (z <= 1.4e-76)
		tmp = t_2;
	elseif (z <= 1.25e+19)
		tmp = y / (t_1 / -z);
	elseif (z <= 1.9e+46)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.55e+22], t$95$3, If[LessEqual[z, -5e-34], t$95$2, If[LessEqual[z, -1.4e-134], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 1.4e-76], t$95$2, If[LessEqual[z, 1.25e+19], N[(y / N[(t$95$1 / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e+46], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.5500000000000001e22 or 1.9e46 < z

   1. Initial program 62.5%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 62.5%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 62.5%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 45.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{t - a \cdot z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 45.8%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(y \cdot z\right)}{t - a \cdot z}} \]

      2. mul-1-neg 45.8%

         \[\leadsto \frac{\color{blue}{-y \cdot z}}{t - a \cdot z} \]

      3. distribute-rgt-neg-out 45.8%

         \[\leadsto \frac{\color{blue}{y \cdot \left(-z\right)}}{t - a \cdot z} \]

      4. associate-/l* 58.1%

         \[\leadsto \color{blue}{\frac{y}{\frac{t - a \cdot z}{-z}}} \]

      5. *-commutative 58.1%

         \[\leadsto \frac{y}{\frac{t - \color{blue}{z \cdot a}}{-z}} \]

   7. Simplified 58.1%

      \[\leadsto \color{blue}{\frac{y}{\frac{t - z \cdot a}{-z}}} \]

   8. Taylor expanded in t around 0 80.4%

      \[\leadsto \frac{y}{\color{blue}{a + -1 \cdot \frac{t}{z}}} \]
   9. Step-by-step derivation

      1. mul-1-neg 80.4%

         \[\leadsto \frac{y}{a + \color{blue}{\left(-\frac{t}{z}\right)}} \]

      2. unsub-neg 80.4%

         \[\leadsto \frac{y}{\color{blue}{a - \frac{t}{z}}} \]

   10. Simplified 80.4%

       \[\leadsto \frac{y}{\color{blue}{a - \frac{t}{z}}} \]

   if -1.5500000000000001e22 < z < -5.0000000000000003e-34 or -1.3999999999999999e-134 < z < 1.40000000000000005e-76 or 1.25e19 < z < 1.9e46

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 84.0%

      \[\leadsto \color{blue}{\frac{x}{t - a \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 84.0%

         \[\leadsto \frac{x}{t - \color{blue}{z \cdot a}} \]

   7. Simplified 84.0%

      \[\leadsto \color{blue}{\frac{x}{t - z \cdot a}} \]

   if -5.0000000000000003e-34 < z < -1.3999999999999999e-134

   1. Initial program 99.9%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.9%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 77.6%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t}} \]

   if 1.40000000000000005e-76 < z < 1.25e19

   1. Initial program 94.6%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 94.6%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 94.6%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 64.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{t - a \cdot z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 64.4%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(y \cdot z\right)}{t - a \cdot z}} \]

      2. mul-1-neg 64.4%

         \[\leadsto \frac{\color{blue}{-y \cdot z}}{t - a \cdot z} \]

      3. distribute-rgt-neg-out 64.4%

         \[\leadsto \frac{\color{blue}{y \cdot \left(-z\right)}}{t - a \cdot z} \]

      4. associate-/l* 59.3%

         \[\leadsto \color{blue}{\frac{y}{\frac{t - a \cdot z}{-z}}} \]

      5. *-commutative 59.3%

         \[\leadsto \frac{y}{\frac{t - \color{blue}{z \cdot a}}{-z}} \]

   7. Simplified 59.3%

      \[\leadsto \color{blue}{\frac{y}{\frac{t - z \cdot a}{-z}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+22}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-34}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-134}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-76}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+19}:\\ \;\;\;\;\frac{y}{\frac{t - z \cdot a}{-z}}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+46}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - z \cdot a\\ t_2 := \frac{x}{t\_1}\\ t_3 := \frac{y}{a - \frac{t}{z}}\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+22}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-34}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-134}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-76}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+15}:\\ \;\;\;\;\frac{z \cdot \left(-y\right)}{t\_1}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+47}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* z a))) (t_2 (/ x t_1)) (t_3 (/ y (- a (/ t z)))))
   (if (<= z -2.4e+22)
     t_3
     (if (<= z -6.4e-34)
       t_2
       (if (<= z -7e-134)
         (/ (- x (* z y)) t)
         (if (<= z 2.3e-76)
           t_2
           (if (<= z 3.1e+15)
             (/ (* z (- y)) t_1)
             (if (<= z 3.3e+47) t_2 t_3))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (z * a);
	double t_2 = x / t_1;
	double t_3 = y / (a - (t / z));
	double tmp;
	if (z <= -2.4e+22) {
		tmp = t_3;
	} else if (z <= -6.4e-34) {
		tmp = t_2;
	} else if (z <= -7e-134) {
		tmp = (x - (z * y)) / t;
	} else if (z <= 2.3e-76) {
		tmp = t_2;
	} else if (z <= 3.1e+15) {
		tmp = (z * -y) / t_1;
	} else if (z <= 3.3e+47) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t - (z * a)
    t_2 = x / t_1
    t_3 = y / (a - (t / z))
    if (z <= (-2.4d+22)) then
        tmp = t_3
    else if (z <= (-6.4d-34)) then
        tmp = t_2
    else if (z <= (-7d-134)) then
        tmp = (x - (z * y)) / t
    else if (z <= 2.3d-76) then
        tmp = t_2
    else if (z <= 3.1d+15) then
        tmp = (z * -y) / t_1
    else if (z <= 3.3d+47) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (z * a);
	double t_2 = x / t_1;
	double t_3 = y / (a - (t / z));
	double tmp;
	if (z <= -2.4e+22) {
		tmp = t_3;
	} else if (z <= -6.4e-34) {
		tmp = t_2;
	} else if (z <= -7e-134) {
		tmp = (x - (z * y)) / t;
	} else if (z <= 2.3e-76) {
		tmp = t_2;
	} else if (z <= 3.1e+15) {
		tmp = (z * -y) / t_1;
	} else if (z <= 3.3e+47) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (z * a)
	t_2 = x / t_1
	t_3 = y / (a - (t / z))
	tmp = 0
	if z <= -2.4e+22:
		tmp = t_3
	elif z <= -6.4e-34:
		tmp = t_2
	elif z <= -7e-134:
		tmp = (x - (z * y)) / t
	elif z <= 2.3e-76:
		tmp = t_2
	elif z <= 3.1e+15:
		tmp = (z * -y) / t_1
	elif z <= 3.3e+47:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(z * a))
	t_2 = Float64(x / t_1)
	t_3 = Float64(y / Float64(a - Float64(t / z)))
	tmp = 0.0
	if (z <= -2.4e+22)
		tmp = t_3;
	elseif (z <= -6.4e-34)
		tmp = t_2;
	elseif (z <= -7e-134)
		tmp = Float64(Float64(x - Float64(z * y)) / t);
	elseif (z <= 2.3e-76)
		tmp = t_2;
	elseif (z <= 3.1e+15)
		tmp = Float64(Float64(z * Float64(-y)) / t_1);
	elseif (z <= 3.3e+47)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (z * a);
	t_2 = x / t_1;
	t_3 = y / (a - (t / z));
	tmp = 0.0;
	if (z <= -2.4e+22)
		tmp = t_3;
	elseif (z <= -6.4e-34)
		tmp = t_2;
	elseif (z <= -7e-134)
		tmp = (x - (z * y)) / t;
	elseif (z <= 2.3e-76)
		tmp = t_2;
	elseif (z <= 3.1e+15)
		tmp = (z * -y) / t_1;
	elseif (z <= 3.3e+47)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.4e+22], t$95$3, If[LessEqual[z, -6.4e-34], t$95$2, If[LessEqual[z, -7e-134], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 2.3e-76], t$95$2, If[LessEqual[z, 3.1e+15], N[(N[(z * (-y)), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[z, 3.3e+47], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.4e22 or 3.2999999999999999e47 < z

   1. Initial program 62.5%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 62.5%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 62.5%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 45.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{t - a \cdot z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 45.8%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(y \cdot z\right)}{t - a \cdot z}} \]

      2. mul-1-neg 45.8%

         \[\leadsto \frac{\color{blue}{-y \cdot z}}{t - a \cdot z} \]

      3. distribute-rgt-neg-out 45.8%

         \[\leadsto \frac{\color{blue}{y \cdot \left(-z\right)}}{t - a \cdot z} \]

      4. associate-/l* 58.1%

         \[\leadsto \color{blue}{\frac{y}{\frac{t - a \cdot z}{-z}}} \]

      5. *-commutative 58.1%

         \[\leadsto \frac{y}{\frac{t - \color{blue}{z \cdot a}}{-z}} \]

   7. Simplified 58.1%

      \[\leadsto \color{blue}{\frac{y}{\frac{t - z \cdot a}{-z}}} \]

   8. Taylor expanded in t around 0 80.4%

      \[\leadsto \frac{y}{\color{blue}{a + -1 \cdot \frac{t}{z}}} \]
   9. Step-by-step derivation

      1. mul-1-neg 80.4%

         \[\leadsto \frac{y}{a + \color{blue}{\left(-\frac{t}{z}\right)}} \]

      2. unsub-neg 80.4%

         \[\leadsto \frac{y}{\color{blue}{a - \frac{t}{z}}} \]

   10. Simplified 80.4%

       \[\leadsto \frac{y}{\color{blue}{a - \frac{t}{z}}} \]

   if -2.4e22 < z < -6.40000000000000005e-34 or -6.9999999999999997e-134 < z < 2.30000000000000006e-76 or 3.1e15 < z < 3.2999999999999999e47

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 84.0%

      \[\leadsto \color{blue}{\frac{x}{t - a \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 84.0%

         \[\leadsto \frac{x}{t - \color{blue}{z \cdot a}} \]

   7. Simplified 84.0%

      \[\leadsto \color{blue}{\frac{x}{t - z \cdot a}} \]

   if -6.40000000000000005e-34 < z < -6.9999999999999997e-134

   1. Initial program 99.9%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.9%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 77.6%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t}} \]

   if 2.30000000000000006e-76 < z < 3.1e15

   1. Initial program 94.6%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 94.6%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 94.6%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 64.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{t - a \cdot z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 64.4%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(y \cdot z\right)}{t - a \cdot z}} \]

      2. associate-*r* 64.4%

         \[\leadsto \frac{\color{blue}{\left(-1 \cdot y\right) \cdot z}}{t - a \cdot z} \]

      3. neg-mul-1 64.4%

         \[\leadsto \frac{\color{blue}{\left(-y\right)} \cdot z}{t - a \cdot z} \]

      4. *-commutative 64.4%

         \[\leadsto \frac{\left(-y\right) \cdot z}{t - \color{blue}{z \cdot a}} \]

   7. Simplified 64.4%

      \[\leadsto \color{blue}{\frac{\left(-y\right) \cdot z}{t - z \cdot a}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+22}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-34}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-134}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-76}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+15}:\\ \;\;\;\;\frac{z \cdot \left(-y\right)}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+47}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 55.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+84}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+25}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{+17}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{+16}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+39}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.6e+84)
   (/ y a)
   (if (<= z -1.55e+25)
     (* y (/ (- z) t))
     (if (<= z -9.2e+17)
       (/ y a)
       (if (<= z 1.22e-39)
         (/ x t)
         (if (<= z 5.1e+16)
           (* z (/ (- y) t))
           (if (<= z 4.4e+39) (/ x t) (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.6e+84) {
		tmp = y / a;
	} else if (z <= -1.55e+25) {
		tmp = y * (-z / t);
	} else if (z <= -9.2e+17) {
		tmp = y / a;
	} else if (z <= 1.22e-39) {
		tmp = x / t;
	} else if (z <= 5.1e+16) {
		tmp = z * (-y / t);
	} else if (z <= 4.4e+39) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.6d+84)) then
        tmp = y / a
    else if (z <= (-1.55d+25)) then
        tmp = y * (-z / t)
    else if (z <= (-9.2d+17)) then
        tmp = y / a
    else if (z <= 1.22d-39) then
        tmp = x / t
    else if (z <= 5.1d+16) then
        tmp = z * (-y / t)
    else if (z <= 4.4d+39) then
        tmp = x / t
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.6e+84) {
		tmp = y / a;
	} else if (z <= -1.55e+25) {
		tmp = y * (-z / t);
	} else if (z <= -9.2e+17) {
		tmp = y / a;
	} else if (z <= 1.22e-39) {
		tmp = x / t;
	} else if (z <= 5.1e+16) {
		tmp = z * (-y / t);
	} else if (z <= 4.4e+39) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.6e+84:
		tmp = y / a
	elif z <= -1.55e+25:
		tmp = y * (-z / t)
	elif z <= -9.2e+17:
		tmp = y / a
	elif z <= 1.22e-39:
		tmp = x / t
	elif z <= 5.1e+16:
		tmp = z * (-y / t)
	elif z <= 4.4e+39:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.6e+84)
		tmp = Float64(y / a);
	elseif (z <= -1.55e+25)
		tmp = Float64(y * Float64(Float64(-z) / t));
	elseif (z <= -9.2e+17)
		tmp = Float64(y / a);
	elseif (z <= 1.22e-39)
		tmp = Float64(x / t);
	elseif (z <= 5.1e+16)
		tmp = Float64(z * Float64(Float64(-y) / t));
	elseif (z <= 4.4e+39)
		tmp = Float64(x / t);
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.6e+84)
		tmp = y / a;
	elseif (z <= -1.55e+25)
		tmp = y * (-z / t);
	elseif (z <= -9.2e+17)
		tmp = y / a;
	elseif (z <= 1.22e-39)
		tmp = x / t;
	elseif (z <= 5.1e+16)
		tmp = z * (-y / t);
	elseif (z <= 4.4e+39)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.6e+84], N[(y / a), $MachinePrecision], If[LessEqual[z, -1.55e+25], N[(y * N[((-z) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9.2e+17], N[(y / a), $MachinePrecision], If[LessEqual[z, 1.22e-39], N[(x / t), $MachinePrecision], If[LessEqual[z, 5.1e+16], N[(z * N[((-y) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4e+39], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.5999999999999998e84 or -1.5499999999999999e25 < z < -9.2e17 or 4.4000000000000003e39 < z

   1. Initial program 61.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 61.8%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 61.8%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 57.7%

      \[\leadsto \color{blue}{\frac{y}{a}} \]

   if -4.5999999999999998e84 < z < -1.5499999999999999e25

   1. Initial program 83.6%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 83.6%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 83.6%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 59.5%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t}} \]

   6. Taylor expanded in x around 0 51.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{t}} \]
   7. Step-by-step derivation

      1. mul-1-neg 51.3%

         \[\leadsto \color{blue}{-\frac{y \cdot z}{t}} \]

      2. *-commutative 51.3%

         \[\leadsto -\frac{\color{blue}{z \cdot y}}{t} \]

      3. associate-*l/ 67.1%

         \[\leadsto -\color{blue}{\frac{z}{t} \cdot y} \]

      4. distribute-rgt-neg-in 67.1%

         \[\leadsto \color{blue}{\frac{z}{t} \cdot \left(-y\right)} \]

   8. Simplified 67.1%

      \[\leadsto \color{blue}{\frac{z}{t} \cdot \left(-y\right)} \]

   if -9.2e17 < z < 1.2200000000000001e-39 or 5.1e16 < z < 4.4000000000000003e39

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 62.6%

      \[\leadsto \color{blue}{\frac{x}{t}} \]

   if 1.2200000000000001e-39 < z < 5.1e16

   1. Initial program 91.7%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 91.7%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 91.7%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 42.9%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t}} \]

   6. Taylor expanded in x around 0 44.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{t}} \]
   7. Step-by-step derivation

      1. associate-*r/ 44.0%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(y \cdot z\right)}{t}} \]

      2. mul-1-neg 44.0%

         \[\leadsto \frac{\color{blue}{-y \cdot z}}{t} \]

   8. Simplified 44.0%

      \[\leadsto \color{blue}{\frac{-y \cdot z}{t}} \]
   9. Step-by-step derivation

      1. div-inv 44.2%

         \[\leadsto \color{blue}{\left(-y \cdot z\right) \cdot \frac{1}{t}} \]

      2. distribute-rgt-neg-in 44.2%

         \[\leadsto \color{blue}{\left(y \cdot \left(-z\right)\right)} \cdot \frac{1}{t} \]

      3. associate-*l* 38.0%

         \[\leadsto \color{blue}{y \cdot \left(\left(-z\right) \cdot \frac{1}{t}\right)} \]

      4. add-sqr-sqrt 0.0%

         \[\leadsto y \cdot \left(\color{blue}{\left(\sqrt{-z} \cdot \sqrt{-z}\right)} \cdot \frac{1}{t}\right) \]

      5. sqrt-unprod 1.9%

         \[\leadsto y \cdot \left(\color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}} \cdot \frac{1}{t}\right) \]

      6. sqr-neg 1.9%

         \[\leadsto y \cdot \left(\sqrt{\color{blue}{z \cdot z}} \cdot \frac{1}{t}\right) \]

      7. sqrt-unprod 1.9%

         \[\leadsto y \cdot \left(\color{blue}{\left(\sqrt{z} \cdot \sqrt{z}\right)} \cdot \frac{1}{t}\right) \]

      8. add-sqr-sqrt 1.9%

         \[\leadsto y \cdot \left(\color{blue}{z} \cdot \frac{1}{t}\right) \]

      9. div-inv 1.9%

         \[\leadsto y \cdot \color{blue}{\frac{z}{t}} \]

   10. Applied egg-rr 1.9%

       \[\leadsto \color{blue}{y \cdot \frac{z}{t}} \]
   11. Step-by-step derivation

       1. associate-*r/ 1.9%

          \[\leadsto \color{blue}{\frac{y \cdot z}{t}} \]

       2. add-sqr-sqrt 0.5%

          \[\leadsto \frac{y \cdot z}{\color{blue}{\sqrt{t} \cdot \sqrt{t}}} \]

       3. sqrt-unprod 18.4%

          \[\leadsto \frac{y \cdot z}{\color{blue}{\sqrt{t \cdot t}}} \]

       4. sqr-neg 18.4%

          \[\leadsto \frac{y \cdot z}{\sqrt{\color{blue}{\left(-t\right) \cdot \left(-t\right)}}} \]

       5. sqrt-unprod 34.1%

          \[\leadsto \frac{y \cdot z}{\color{blue}{\sqrt{-t} \cdot \sqrt{-t}}} \]

       6. add-sqr-sqrt 44.0%

          \[\leadsto \frac{y \cdot z}{\color{blue}{-t}} \]

       7. associate-*l/ 44.0%

          \[\leadsto \color{blue}{\frac{y}{-t} \cdot z} \]

       8. associate-/r/ 35.7%

          \[\leadsto \color{blue}{\frac{y}{\frac{-t}{z}}} \]

       9. frac-2neg 35.7%

          \[\leadsto \color{blue}{\frac{-y}{-\frac{-t}{z}}} \]

       10. distribute-neg-frac 35.7%

           \[\leadsto \frac{-y}{\color{blue}{\frac{-\left(-t\right)}{z}}} \]

       11. remove-double-neg 35.7%

           \[\leadsto \frac{-y}{\frac{\color{blue}{t}}{z}} \]

       12. distribute-frac-neg 35.7%

           \[\leadsto \color{blue}{-\frac{y}{\frac{t}{z}}} \]

       13. associate-/l* 44.0%

           \[\leadsto -\color{blue}{\frac{y \cdot z}{t}} \]

       14. add-sqr-sqrt 9.5%

           \[\leadsto -\frac{y \cdot z}{\color{blue}{\sqrt{t} \cdot \sqrt{t}}} \]

       15. sqrt-unprod 11.4%

           \[\leadsto -\frac{y \cdot z}{\color{blue}{\sqrt{t \cdot t}}} \]

       16. sqr-neg 11.4%

           \[\leadsto -\frac{y \cdot z}{\sqrt{\color{blue}{\left(-t\right) \cdot \left(-t\right)}}} \]

       17. sqrt-unprod 1.4%

           \[\leadsto -\frac{y \cdot z}{\color{blue}{\sqrt{-t} \cdot \sqrt{-t}}} \]

       18. add-sqr-sqrt 1.9%

           \[\leadsto -\frac{y \cdot z}{\color{blue}{-t}} \]

       19. associate-*l/ 1.9%

           \[\leadsto -\color{blue}{\frac{y}{-t} \cdot z} \]

       20. *-commutative 1.9%

           \[\leadsto -\color{blue}{z \cdot \frac{y}{-t}} \]

       21. add-sqr-sqrt 1.4%

           \[\leadsto -z \cdot \frac{y}{\color{blue}{\sqrt{-t} \cdot \sqrt{-t}}} \]

       22. sqrt-unprod 11.4%

           \[\leadsto -z \cdot \frac{y}{\color{blue}{\sqrt{\left(-t\right) \cdot \left(-t\right)}}} \]

       23. sqr-neg 11.4%

           \[\leadsto -z \cdot \frac{y}{\sqrt{\color{blue}{t \cdot t}}} \]

       24. sqrt-unprod 9.5%

           \[\leadsto -z \cdot \frac{y}{\color{blue}{\sqrt{t} \cdot \sqrt{t}}} \]

       25. add-sqr-sqrt 44.0%

           \[\leadsto -z \cdot \frac{y}{\color{blue}{t}} \]

   12. Applied egg-rr 44.0%

       \[\leadsto \color{blue}{-z \cdot \frac{y}{t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+84}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+25}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{+17}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{+16}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+39}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 55.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+86}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{+29}:\\ \;\;\;\;\frac{y}{\frac{-t}{z}}\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{+17}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+14}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq 10^{+41}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.5e+86)
   (/ y a)
   (if (<= z -3.9e+29)
     (/ y (/ (- t) z))
     (if (<= z -9.2e+17)
       (/ y a)
       (if (<= z 5.5e-40)
         (/ x t)
         (if (<= z 3.8e+14)
           (* z (/ (- y) t))
           (if (<= z 1e+41) (/ x t) (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.5e+86) {
		tmp = y / a;
	} else if (z <= -3.9e+29) {
		tmp = y / (-t / z);
	} else if (z <= -9.2e+17) {
		tmp = y / a;
	} else if (z <= 5.5e-40) {
		tmp = x / t;
	} else if (z <= 3.8e+14) {
		tmp = z * (-y / t);
	} else if (z <= 1e+41) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-7.5d+86)) then
        tmp = y / a
    else if (z <= (-3.9d+29)) then
        tmp = y / (-t / z)
    else if (z <= (-9.2d+17)) then
        tmp = y / a
    else if (z <= 5.5d-40) then
        tmp = x / t
    else if (z <= 3.8d+14) then
        tmp = z * (-y / t)
    else if (z <= 1d+41) then
        tmp = x / t
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.5e+86) {
		tmp = y / a;
	} else if (z <= -3.9e+29) {
		tmp = y / (-t / z);
	} else if (z <= -9.2e+17) {
		tmp = y / a;
	} else if (z <= 5.5e-40) {
		tmp = x / t;
	} else if (z <= 3.8e+14) {
		tmp = z * (-y / t);
	} else if (z <= 1e+41) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.5e+86:
		tmp = y / a
	elif z <= -3.9e+29:
		tmp = y / (-t / z)
	elif z <= -9.2e+17:
		tmp = y / a
	elif z <= 5.5e-40:
		tmp = x / t
	elif z <= 3.8e+14:
		tmp = z * (-y / t)
	elif z <= 1e+41:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.5e+86)
		tmp = Float64(y / a);
	elseif (z <= -3.9e+29)
		tmp = Float64(y / Float64(Float64(-t) / z));
	elseif (z <= -9.2e+17)
		tmp = Float64(y / a);
	elseif (z <= 5.5e-40)
		tmp = Float64(x / t);
	elseif (z <= 3.8e+14)
		tmp = Float64(z * Float64(Float64(-y) / t));
	elseif (z <= 1e+41)
		tmp = Float64(x / t);
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7.5e+86)
		tmp = y / a;
	elseif (z <= -3.9e+29)
		tmp = y / (-t / z);
	elseif (z <= -9.2e+17)
		tmp = y / a;
	elseif (z <= 5.5e-40)
		tmp = x / t;
	elseif (z <= 3.8e+14)
		tmp = z * (-y / t);
	elseif (z <= 1e+41)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.5e+86], N[(y / a), $MachinePrecision], If[LessEqual[z, -3.9e+29], N[(y / N[((-t) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9.2e+17], N[(y / a), $MachinePrecision], If[LessEqual[z, 5.5e-40], N[(x / t), $MachinePrecision], If[LessEqual[z, 3.8e+14], N[(z * N[((-y) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e+41], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.4999999999999997e86 or -3.89999999999999968e29 < z < -9.2e17 or 1.00000000000000001e41 < z

   1. Initial program 61.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 61.8%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 61.8%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 57.7%

      \[\leadsto \color{blue}{\frac{y}{a}} \]

   if -7.4999999999999997e86 < z < -3.89999999999999968e29

   1. Initial program 83.6%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 83.6%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 83.6%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 67.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{t - a \cdot z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 67.5%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(y \cdot z\right)}{t - a \cdot z}} \]

      2. mul-1-neg 67.5%

         \[\leadsto \frac{\color{blue}{-y \cdot z}}{t - a \cdot z} \]

      3. distribute-rgt-neg-out 67.5%

         \[\leadsto \frac{\color{blue}{y \cdot \left(-z\right)}}{t - a \cdot z} \]

      4. associate-/l* 83.9%

         \[\leadsto \color{blue}{\frac{y}{\frac{t - a \cdot z}{-z}}} \]

      5. *-commutative 83.9%

         \[\leadsto \frac{y}{\frac{t - \color{blue}{z \cdot a}}{-z}} \]

   7. Simplified 83.9%

      \[\leadsto \color{blue}{\frac{y}{\frac{t - z \cdot a}{-z}}} \]

   8. Taylor expanded in t around inf 67.5%

      \[\leadsto \frac{y}{\color{blue}{-1 \cdot \frac{t}{z}}} \]
   9. Step-by-step derivation

      1. associate-*r/ 67.5%

         \[\leadsto \frac{y}{\color{blue}{\frac{-1 \cdot t}{z}}} \]

      2. neg-mul-1 67.5%

         \[\leadsto \frac{y}{\frac{\color{blue}{-t}}{z}} \]

   10. Simplified 67.5%

       \[\leadsto \frac{y}{\color{blue}{\frac{-t}{z}}} \]

   if -9.2e17 < z < 5.50000000000000002e-40 or 3.8e14 < z < 1.00000000000000001e41

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 62.6%

      \[\leadsto \color{blue}{\frac{x}{t}} \]

   if 5.50000000000000002e-40 < z < 3.8e14

   1. Initial program 91.7%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 91.7%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 91.7%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 42.9%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t}} \]

   6. Taylor expanded in x around 0 44.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{t}} \]
   7. Step-by-step derivation

      1. associate-*r/ 44.0%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(y \cdot z\right)}{t}} \]

      2. mul-1-neg 44.0%

         \[\leadsto \frac{\color{blue}{-y \cdot z}}{t} \]

   8. Simplified 44.0%

      \[\leadsto \color{blue}{\frac{-y \cdot z}{t}} \]
   9. Step-by-step derivation

      1. div-inv 44.2%

         \[\leadsto \color{blue}{\left(-y \cdot z\right) \cdot \frac{1}{t}} \]

      2. distribute-rgt-neg-in 44.2%

         \[\leadsto \color{blue}{\left(y \cdot \left(-z\right)\right)} \cdot \frac{1}{t} \]

      3. associate-*l* 38.0%

         \[\leadsto \color{blue}{y \cdot \left(\left(-z\right) \cdot \frac{1}{t}\right)} \]

      4. add-sqr-sqrt 0.0%

         \[\leadsto y \cdot \left(\color{blue}{\left(\sqrt{-z} \cdot \sqrt{-z}\right)} \cdot \frac{1}{t}\right) \]

      5. sqrt-unprod 1.9%

         \[\leadsto y \cdot \left(\color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}} \cdot \frac{1}{t}\right) \]

      6. sqr-neg 1.9%

         \[\leadsto y \cdot \left(\sqrt{\color{blue}{z \cdot z}} \cdot \frac{1}{t}\right) \]

      7. sqrt-unprod 1.9%

         \[\leadsto y \cdot \left(\color{blue}{\left(\sqrt{z} \cdot \sqrt{z}\right)} \cdot \frac{1}{t}\right) \]

      8. add-sqr-sqrt 1.9%

         \[\leadsto y \cdot \left(\color{blue}{z} \cdot \frac{1}{t}\right) \]

      9. div-inv 1.9%

         \[\leadsto y \cdot \color{blue}{\frac{z}{t}} \]

   10. Applied egg-rr 1.9%

       \[\leadsto \color{blue}{y \cdot \frac{z}{t}} \]
   11. Step-by-step derivation

       1. associate-*r/ 1.9%

          \[\leadsto \color{blue}{\frac{y \cdot z}{t}} \]

       2. add-sqr-sqrt 0.5%

          \[\leadsto \frac{y \cdot z}{\color{blue}{\sqrt{t} \cdot \sqrt{t}}} \]

       3. sqrt-unprod 18.4%

          \[\leadsto \frac{y \cdot z}{\color{blue}{\sqrt{t \cdot t}}} \]

       4. sqr-neg 18.4%

          \[\leadsto \frac{y \cdot z}{\sqrt{\color{blue}{\left(-t\right) \cdot \left(-t\right)}}} \]

       5. sqrt-unprod 34.1%

          \[\leadsto \frac{y \cdot z}{\color{blue}{\sqrt{-t} \cdot \sqrt{-t}}} \]

       6. add-sqr-sqrt 44.0%

          \[\leadsto \frac{y \cdot z}{\color{blue}{-t}} \]

       7. associate-*l/ 44.0%

          \[\leadsto \color{blue}{\frac{y}{-t} \cdot z} \]

       8. associate-/r/ 35.7%

          \[\leadsto \color{blue}{\frac{y}{\frac{-t}{z}}} \]

       9. frac-2neg 35.7%

          \[\leadsto \color{blue}{\frac{-y}{-\frac{-t}{z}}} \]

       10. distribute-neg-frac 35.7%

           \[\leadsto \frac{-y}{\color{blue}{\frac{-\left(-t\right)}{z}}} \]

       11. remove-double-neg 35.7%

           \[\leadsto \frac{-y}{\frac{\color{blue}{t}}{z}} \]

       12. distribute-frac-neg 35.7%

           \[\leadsto \color{blue}{-\frac{y}{\frac{t}{z}}} \]

       13. associate-/l* 44.0%

           \[\leadsto -\color{blue}{\frac{y \cdot z}{t}} \]

       14. add-sqr-sqrt 9.5%

           \[\leadsto -\frac{y \cdot z}{\color{blue}{\sqrt{t} \cdot \sqrt{t}}} \]

       15. sqrt-unprod 11.4%

           \[\leadsto -\frac{y \cdot z}{\color{blue}{\sqrt{t \cdot t}}} \]

       16. sqr-neg 11.4%

           \[\leadsto -\frac{y \cdot z}{\sqrt{\color{blue}{\left(-t\right) \cdot \left(-t\right)}}} \]

       17. sqrt-unprod 1.4%

           \[\leadsto -\frac{y \cdot z}{\color{blue}{\sqrt{-t} \cdot \sqrt{-t}}} \]

       18. add-sqr-sqrt 1.9%

           \[\leadsto -\frac{y \cdot z}{\color{blue}{-t}} \]

       19. associate-*l/ 1.9%

           \[\leadsto -\color{blue}{\frac{y}{-t} \cdot z} \]

       20. *-commutative 1.9%

           \[\leadsto -\color{blue}{z \cdot \frac{y}{-t}} \]

       21. add-sqr-sqrt 1.4%

           \[\leadsto -z \cdot \frac{y}{\color{blue}{\sqrt{-t} \cdot \sqrt{-t}}} \]

       22. sqrt-unprod 11.4%

           \[\leadsto -z \cdot \frac{y}{\color{blue}{\sqrt{\left(-t\right) \cdot \left(-t\right)}}} \]

       23. sqr-neg 11.4%

           \[\leadsto -z \cdot \frac{y}{\sqrt{\color{blue}{t \cdot t}}} \]

       24. sqrt-unprod 9.5%

           \[\leadsto -z \cdot \frac{y}{\color{blue}{\sqrt{t} \cdot \sqrt{t}}} \]

       25. add-sqr-sqrt 44.0%

           \[\leadsto -z \cdot \frac{y}{\color{blue}{t}} \]

   12. Applied egg-rr 44.0%

       \[\leadsto \color{blue}{-z \cdot \frac{y}{t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+86}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{+29}:\\ \;\;\;\;\frac{y}{\frac{-t}{z}}\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{+17}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+14}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq 10^{+41}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 54.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+84}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{+25}:\\ \;\;\;\;\frac{y}{\frac{-t}{z}}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+17}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-49}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+20}:\\ \;\;\;\;\frac{\frac{-x}{a}}{z}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+39}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.2e+84)
   (/ y a)
   (if (<= z -6.6e+25)
     (/ y (/ (- t) z))
     (if (<= z -6e+17)
       (/ y a)
       (if (<= z 5e-49)
         (/ x t)
         (if (<= z 2.2e+20)
           (/ (/ (- x) a) z)
           (if (<= z 4.8e+39) (/ x t) (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.2e+84) {
		tmp = y / a;
	} else if (z <= -6.6e+25) {
		tmp = y / (-t / z);
	} else if (z <= -6e+17) {
		tmp = y / a;
	} else if (z <= 5e-49) {
		tmp = x / t;
	} else if (z <= 2.2e+20) {
		tmp = (-x / a) / z;
	} else if (z <= 4.8e+39) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.2d+84)) then
        tmp = y / a
    else if (z <= (-6.6d+25)) then
        tmp = y / (-t / z)
    else if (z <= (-6d+17)) then
        tmp = y / a
    else if (z <= 5d-49) then
        tmp = x / t
    else if (z <= 2.2d+20) then
        tmp = (-x / a) / z
    else if (z <= 4.8d+39) then
        tmp = x / t
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.2e+84) {
		tmp = y / a;
	} else if (z <= -6.6e+25) {
		tmp = y / (-t / z);
	} else if (z <= -6e+17) {
		tmp = y / a;
	} else if (z <= 5e-49) {
		tmp = x / t;
	} else if (z <= 2.2e+20) {
		tmp = (-x / a) / z;
	} else if (z <= 4.8e+39) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.2e+84:
		tmp = y / a
	elif z <= -6.6e+25:
		tmp = y / (-t / z)
	elif z <= -6e+17:
		tmp = y / a
	elif z <= 5e-49:
		tmp = x / t
	elif z <= 2.2e+20:
		tmp = (-x / a) / z
	elif z <= 4.8e+39:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.2e+84)
		tmp = Float64(y / a);
	elseif (z <= -6.6e+25)
		tmp = Float64(y / Float64(Float64(-t) / z));
	elseif (z <= -6e+17)
		tmp = Float64(y / a);
	elseif (z <= 5e-49)
		tmp = Float64(x / t);
	elseif (z <= 2.2e+20)
		tmp = Float64(Float64(Float64(-x) / a) / z);
	elseif (z <= 4.8e+39)
		tmp = Float64(x / t);
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.2e+84)
		tmp = y / a;
	elseif (z <= -6.6e+25)
		tmp = y / (-t / z);
	elseif (z <= -6e+17)
		tmp = y / a;
	elseif (z <= 5e-49)
		tmp = x / t;
	elseif (z <= 2.2e+20)
		tmp = (-x / a) / z;
	elseif (z <= 4.8e+39)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.2e+84], N[(y / a), $MachinePrecision], If[LessEqual[z, -6.6e+25], N[(y / N[((-t) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6e+17], N[(y / a), $MachinePrecision], If[LessEqual[z, 5e-49], N[(x / t), $MachinePrecision], If[LessEqual[z, 2.2e+20], N[(N[((-x) / a), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 4.8e+39], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.20000000000000037e84 or -6.6000000000000002e25 < z < -6e17 or 4.8000000000000002e39 < z

   1. Initial program 61.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 61.8%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 61.8%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 57.7%

      \[\leadsto \color{blue}{\frac{y}{a}} \]

   if -4.20000000000000037e84 < z < -6.6000000000000002e25

   1. Initial program 83.6%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 83.6%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 83.6%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 67.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{t - a \cdot z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 67.5%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(y \cdot z\right)}{t - a \cdot z}} \]

      2. mul-1-neg 67.5%

         \[\leadsto \frac{\color{blue}{-y \cdot z}}{t - a \cdot z} \]

      3. distribute-rgt-neg-out 67.5%

         \[\leadsto \frac{\color{blue}{y \cdot \left(-z\right)}}{t - a \cdot z} \]

      4. associate-/l* 83.9%

         \[\leadsto \color{blue}{\frac{y}{\frac{t - a \cdot z}{-z}}} \]

      5. *-commutative 83.9%

         \[\leadsto \frac{y}{\frac{t - \color{blue}{z \cdot a}}{-z}} \]

   7. Simplified 83.9%

      \[\leadsto \color{blue}{\frac{y}{\frac{t - z \cdot a}{-z}}} \]

   8. Taylor expanded in t around inf 67.5%

      \[\leadsto \frac{y}{\color{blue}{-1 \cdot \frac{t}{z}}} \]
   9. Step-by-step derivation

      1. associate-*r/ 67.5%

         \[\leadsto \frac{y}{\color{blue}{\frac{-1 \cdot t}{z}}} \]

      2. neg-mul-1 67.5%

         \[\leadsto \frac{y}{\frac{\color{blue}{-t}}{z}} \]

   10. Simplified 67.5%

       \[\leadsto \frac{y}{\color{blue}{\frac{-t}{z}}} \]

   if -6e17 < z < 4.9999999999999999e-49 or 2.2e20 < z < 4.8000000000000002e39

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 63.5%

      \[\leadsto \color{blue}{\frac{x}{t}} \]

   if 4.9999999999999999e-49 < z < 2.2e20

   1. Initial program 92.9%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 92.9%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 92.9%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 92.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{t - z \cdot a}{x - y \cdot z}}} \]

      2. associate-/r/ 92.7%

         \[\leadsto \color{blue}{\frac{1}{t - z \cdot a} \cdot \left(x - y \cdot z\right)} \]

      3. sub-neg 92.7%

         \[\leadsto \frac{1}{\color{blue}{t + \left(-z \cdot a\right)}} \cdot \left(x - y \cdot z\right) \]

      4. +-commutative 92.7%

         \[\leadsto \frac{1}{\color{blue}{\left(-z \cdot a\right) + t}} \cdot \left(x - y \cdot z\right) \]

      5. *-commutative 92.7%

         \[\leadsto \frac{1}{\left(-\color{blue}{a \cdot z}\right) + t} \cdot \left(x - y \cdot z\right) \]

      6. distribute-rgt-neg-in 92.7%

         \[\leadsto \frac{1}{\color{blue}{a \cdot \left(-z\right)} + t} \cdot \left(x - y \cdot z\right) \]

      7. fma-def 92.7%

         \[\leadsto \frac{1}{\color{blue}{\mathsf{fma}\left(a, -z, t\right)}} \cdot \left(x - y \cdot z\right) \]

   6. Applied egg-rr 92.7%

      \[\leadsto \color{blue}{\frac{1}{\mathsf{fma}\left(a, -z, t\right)} \cdot \left(x - y \cdot z\right)} \]

   7. Taylor expanded in a around inf 57.8%

      \[\leadsto \color{blue}{\frac{-1}{a \cdot z}} \cdot \left(x - y \cdot z\right) \]
   8. Step-by-step derivation

      1. *-commutative 57.8%

         \[\leadsto \frac{-1}{\color{blue}{z \cdot a}} \cdot \left(x - y \cdot z\right) \]

   9. Simplified 57.8%

      \[\leadsto \color{blue}{\frac{-1}{z \cdot a}} \cdot \left(x - y \cdot z\right) \]

   10. Taylor expanded in z around 0 31.8%

       \[\leadsto \color{blue}{-1 \cdot \frac{x}{a \cdot z}} \]
   11. Step-by-step derivation

       1. mul-1-neg 31.8%

          \[\leadsto \color{blue}{-\frac{x}{a \cdot z}} \]

       2. associate-/r* 38.7%

          \[\leadsto -\color{blue}{\frac{\frac{x}{a}}{z}} \]

       3. distribute-frac-neg 38.7%

          \[\leadsto \color{blue}{\frac{-\frac{x}{a}}{z}} \]

       4. mul-1-neg 38.7%

          \[\leadsto \frac{\color{blue}{-1 \cdot \frac{x}{a}}}{z} \]

       5. associate-*r/ 38.7%

          \[\leadsto \frac{\color{blue}{\frac{-1 \cdot x}{a}}}{z} \]

       6. neg-mul-1 38.7%

          \[\leadsto \frac{\frac{\color{blue}{-x}}{a}}{z} \]

   12. Simplified 38.7%

       \[\leadsto \color{blue}{\frac{\frac{-x}{a}}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+84}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{+25}:\\ \;\;\;\;\frac{y}{\frac{-t}{z}}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+17}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-49}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+20}:\\ \;\;\;\;\frac{\frac{-x}{a}}{z}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+39}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.25 \cdot 10^{+22} \lor \neg \left(z \leq 2.25 \cdot 10^{-76} \lor \neg \left(z \leq 1.9 \cdot 10^{+16}\right) \land z \leq 2 \cdot 10^{+46}\right):\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.25e+22)
         (not (or (<= z 2.25e-76) (and (not (<= z 1.9e+16)) (<= z 2e+46)))))
   (/ y (- a (/ t z)))
   (/ x (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.25e+22) || !((z <= 2.25e-76) || (!(z <= 1.9e+16) && (z <= 2e+46)))) {
		tmp = y / (a - (t / z));
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3.25d+22)) .or. (.not. (z <= 2.25d-76) .or. (.not. (z <= 1.9d+16)) .and. (z <= 2d+46))) then
        tmp = y / (a - (t / z))
    else
        tmp = x / (t - (z * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.25e+22) || !((z <= 2.25e-76) || (!(z <= 1.9e+16) && (z <= 2e+46)))) {
		tmp = y / (a - (t / z));
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.25e+22) or not ((z <= 2.25e-76) or (not (z <= 1.9e+16) and (z <= 2e+46))):
		tmp = y / (a - (t / z))
	else:
		tmp = x / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.25e+22) || !((z <= 2.25e-76) || (!(z <= 1.9e+16) && (z <= 2e+46))))
		tmp = Float64(y / Float64(a - Float64(t / z)));
	else
		tmp = Float64(x / Float64(t - Float64(z * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.25e+22) || ~(((z <= 2.25e-76) || (~((z <= 1.9e+16)) && (z <= 2e+46)))))
		tmp = y / (a - (t / z));
	else
		tmp = x / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.25e+22], N[Not[Or[LessEqual[z, 2.25e-76], And[N[Not[LessEqual[z, 1.9e+16]], $MachinePrecision], LessEqual[z, 2e+46]]]], $MachinePrecision]], N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2499999999999999e22 or 2.25e-76 < z < 1.9e16 or 2e46 < z

   1. Initial program 67.6%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 67.6%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 67.6%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 48.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{t - a \cdot z}} \]
   6. Step-by-step derivation

      1. associate-*r/ 48.7%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(y \cdot z\right)}{t - a \cdot z}} \]

      2. mul-1-neg 48.7%

         \[\leadsto \frac{\color{blue}{-y \cdot z}}{t - a \cdot z} \]

      3. distribute-rgt-neg-out 48.7%

         \[\leadsto \frac{\color{blue}{y \cdot \left(-z\right)}}{t - a \cdot z} \]

      4. associate-/l* 58.3%

         \[\leadsto \color{blue}{\frac{y}{\frac{t - a \cdot z}{-z}}} \]

      5. *-commutative 58.3%

         \[\leadsto \frac{y}{\frac{t - \color{blue}{z \cdot a}}{-z}} \]

   7. Simplified 58.3%

      \[\leadsto \color{blue}{\frac{y}{\frac{t - z \cdot a}{-z}}} \]

   8. Taylor expanded in t around 0 77.1%

      \[\leadsto \frac{y}{\color{blue}{a + -1 \cdot \frac{t}{z}}} \]
   9. Step-by-step derivation

      1. mul-1-neg 77.1%

         \[\leadsto \frac{y}{a + \color{blue}{\left(-\frac{t}{z}\right)}} \]

      2. unsub-neg 77.1%

         \[\leadsto \frac{y}{\color{blue}{a - \frac{t}{z}}} \]

   10. Simplified 77.1%

       \[\leadsto \frac{y}{\color{blue}{a - \frac{t}{z}}} \]

   if -3.2499999999999999e22 < z < 2.25e-76 or 1.9e16 < z < 2e46

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 79.3%

      \[\leadsto \color{blue}{\frac{x}{t - a \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 79.3%

         \[\leadsto \frac{x}{t - \color{blue}{z \cdot a}} \]

   7. Simplified 79.3%

      \[\leadsto \color{blue}{\frac{x}{t - z \cdot a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.25 \cdot 10^{+22} \lor \neg \left(z \leq 2.25 \cdot 10^{-76} \lor \neg \left(z \leq 1.9 \cdot 10^{+16}\right) \land z \leq 2 \cdot 10^{+46}\right):\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 55.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+50}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+18}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.8e+50)
   (/ y a)
   (if (<= z 6e-39)
     (/ x t)
     (if (<= z 3.3e+18)
       (* z (/ (- y) t))
       (if (<= z 5.6e+40) (/ x t) (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.8e+50) {
		tmp = y / a;
	} else if (z <= 6e-39) {
		tmp = x / t;
	} else if (z <= 3.3e+18) {
		tmp = z * (-y / t);
	} else if (z <= 5.6e+40) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.8d+50)) then
        tmp = y / a
    else if (z <= 6d-39) then
        tmp = x / t
    else if (z <= 3.3d+18) then
        tmp = z * (-y / t)
    else if (z <= 5.6d+40) then
        tmp = x / t
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.8e+50) {
		tmp = y / a;
	} else if (z <= 6e-39) {
		tmp = x / t;
	} else if (z <= 3.3e+18) {
		tmp = z * (-y / t);
	} else if (z <= 5.6e+40) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.8e+50:
		tmp = y / a
	elif z <= 6e-39:
		tmp = x / t
	elif z <= 3.3e+18:
		tmp = z * (-y / t)
	elif z <= 5.6e+40:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.8e+50)
		tmp = Float64(y / a);
	elseif (z <= 6e-39)
		tmp = Float64(x / t);
	elseif (z <= 3.3e+18)
		tmp = Float64(z * Float64(Float64(-y) / t));
	elseif (z <= 5.6e+40)
		tmp = Float64(x / t);
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.8e+50)
		tmp = y / a;
	elseif (z <= 6e-39)
		tmp = x / t;
	elseif (z <= 3.3e+18)
		tmp = z * (-y / t);
	elseif (z <= 5.6e+40)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.8e+50], N[(y / a), $MachinePrecision], If[LessEqual[z, 6e-39], N[(x / t), $MachinePrecision], If[LessEqual[z, 3.3e+18], N[(z * N[((-y) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.6e+40], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.8000000000000004e50 or 5.6000000000000003e40 < z

   1. Initial program 61.0%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 61.0%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 61.0%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 56.1%

      \[\leadsto \color{blue}{\frac{y}{a}} \]

   if -4.8000000000000004e50 < z < 6.00000000000000055e-39 or 3.3e18 < z < 5.6000000000000003e40

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 61.1%

      \[\leadsto \color{blue}{\frac{x}{t}} \]

   if 6.00000000000000055e-39 < z < 3.3e18

   1. Initial program 91.7%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 91.7%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 91.7%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 42.9%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t}} \]

   6. Taylor expanded in x around 0 44.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{t}} \]
   7. Step-by-step derivation

      1. associate-*r/ 44.0%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(y \cdot z\right)}{t}} \]

      2. mul-1-neg 44.0%

         \[\leadsto \frac{\color{blue}{-y \cdot z}}{t} \]

   8. Simplified 44.0%

      \[\leadsto \color{blue}{\frac{-y \cdot z}{t}} \]
   9. Step-by-step derivation

      1. div-inv 44.2%

         \[\leadsto \color{blue}{\left(-y \cdot z\right) \cdot \frac{1}{t}} \]

      2. distribute-rgt-neg-in 44.2%

         \[\leadsto \color{blue}{\left(y \cdot \left(-z\right)\right)} \cdot \frac{1}{t} \]

      3. associate-*l* 38.0%

         \[\leadsto \color{blue}{y \cdot \left(\left(-z\right) \cdot \frac{1}{t}\right)} \]

      4. add-sqr-sqrt 0.0%

         \[\leadsto y \cdot \left(\color{blue}{\left(\sqrt{-z} \cdot \sqrt{-z}\right)} \cdot \frac{1}{t}\right) \]

      5. sqrt-unprod 1.9%

         \[\leadsto y \cdot \left(\color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}} \cdot \frac{1}{t}\right) \]

      6. sqr-neg 1.9%

         \[\leadsto y \cdot \left(\sqrt{\color{blue}{z \cdot z}} \cdot \frac{1}{t}\right) \]

      7. sqrt-unprod 1.9%

         \[\leadsto y \cdot \left(\color{blue}{\left(\sqrt{z} \cdot \sqrt{z}\right)} \cdot \frac{1}{t}\right) \]

      8. add-sqr-sqrt 1.9%

         \[\leadsto y \cdot \left(\color{blue}{z} \cdot \frac{1}{t}\right) \]

      9. div-inv 1.9%

         \[\leadsto y \cdot \color{blue}{\frac{z}{t}} \]

   10. Applied egg-rr 1.9%

       \[\leadsto \color{blue}{y \cdot \frac{z}{t}} \]
   11. Step-by-step derivation

       1. associate-*r/ 1.9%

          \[\leadsto \color{blue}{\frac{y \cdot z}{t}} \]

       2. add-sqr-sqrt 0.5%

          \[\leadsto \frac{y \cdot z}{\color{blue}{\sqrt{t} \cdot \sqrt{t}}} \]

       3. sqrt-unprod 18.4%

          \[\leadsto \frac{y \cdot z}{\color{blue}{\sqrt{t \cdot t}}} \]

       4. sqr-neg 18.4%

          \[\leadsto \frac{y \cdot z}{\sqrt{\color{blue}{\left(-t\right) \cdot \left(-t\right)}}} \]

       5. sqrt-unprod 34.1%

          \[\leadsto \frac{y \cdot z}{\color{blue}{\sqrt{-t} \cdot \sqrt{-t}}} \]

       6. add-sqr-sqrt 44.0%

          \[\leadsto \frac{y \cdot z}{\color{blue}{-t}} \]

       7. associate-*l/ 44.0%

          \[\leadsto \color{blue}{\frac{y}{-t} \cdot z} \]

       8. associate-/r/ 35.7%

          \[\leadsto \color{blue}{\frac{y}{\frac{-t}{z}}} \]

       9. frac-2neg 35.7%

          \[\leadsto \color{blue}{\frac{-y}{-\frac{-t}{z}}} \]

       10. distribute-neg-frac 35.7%

           \[\leadsto \frac{-y}{\color{blue}{\frac{-\left(-t\right)}{z}}} \]

       11. remove-double-neg 35.7%

           \[\leadsto \frac{-y}{\frac{\color{blue}{t}}{z}} \]

       12. distribute-frac-neg 35.7%

           \[\leadsto \color{blue}{-\frac{y}{\frac{t}{z}}} \]

       13. associate-/l* 44.0%

           \[\leadsto -\color{blue}{\frac{y \cdot z}{t}} \]

       14. add-sqr-sqrt 9.5%

           \[\leadsto -\frac{y \cdot z}{\color{blue}{\sqrt{t} \cdot \sqrt{t}}} \]

       15. sqrt-unprod 11.4%

           \[\leadsto -\frac{y \cdot z}{\color{blue}{\sqrt{t \cdot t}}} \]

       16. sqr-neg 11.4%

           \[\leadsto -\frac{y \cdot z}{\sqrt{\color{blue}{\left(-t\right) \cdot \left(-t\right)}}} \]

       17. sqrt-unprod 1.4%

           \[\leadsto -\frac{y \cdot z}{\color{blue}{\sqrt{-t} \cdot \sqrt{-t}}} \]

       18. add-sqr-sqrt 1.9%

           \[\leadsto -\frac{y \cdot z}{\color{blue}{-t}} \]

       19. associate-*l/ 1.9%

           \[\leadsto -\color{blue}{\frac{y}{-t} \cdot z} \]

       20. *-commutative 1.9%

           \[\leadsto -\color{blue}{z \cdot \frac{y}{-t}} \]

       21. add-sqr-sqrt 1.4%

           \[\leadsto -z \cdot \frac{y}{\color{blue}{\sqrt{-t} \cdot \sqrt{-t}}} \]

       22. sqrt-unprod 11.4%

           \[\leadsto -z \cdot \frac{y}{\color{blue}{\sqrt{\left(-t\right) \cdot \left(-t\right)}}} \]

       23. sqr-neg 11.4%

           \[\leadsto -z \cdot \frac{y}{\sqrt{\color{blue}{t \cdot t}}} \]

       24. sqrt-unprod 9.5%

           \[\leadsto -z \cdot \frac{y}{\color{blue}{\sqrt{t} \cdot \sqrt{t}}} \]

       25. add-sqr-sqrt 44.0%

           \[\leadsto -z \cdot \frac{y}{\color{blue}{t}} \]

   12. Applied egg-rr 44.0%

       \[\leadsto \color{blue}{-z \cdot \frac{y}{t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+50}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+18}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+51} \lor \neg \left(z \leq 8 \cdot 10^{+52}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.2e+51) (not (<= z 8e+52))) (/ y a) (/ x (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.2e+51) || !(z <= 8e+52)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3.2d+51)) .or. (.not. (z <= 8d+52))) then
        tmp = y / a
    else
        tmp = x / (t - (z * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.2e+51) || !(z <= 8e+52)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.2e+51) or not (z <= 8e+52):
		tmp = y / a
	else:
		tmp = x / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.2e+51) || !(z <= 8e+52))
		tmp = Float64(y / a);
	else
		tmp = Float64(x / Float64(t - Float64(z * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.2e+51) || ~((z <= 8e+52)))
		tmp = y / a;
	else
		tmp = x / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.2e+51], N[Not[LessEqual[z, 8e+52]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2000000000000002e51 or 7.9999999999999999e52 < z

   1. Initial program 60.6%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 60.6%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 60.6%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 56.6%

      \[\leadsto \color{blue}{\frac{y}{a}} \]

   if -3.2000000000000002e51 < z < 7.9999999999999999e52

   1. Initial program 99.2%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.2%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 99.2%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 72.7%

      \[\leadsto \color{blue}{\frac{x}{t - a \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 72.7%

         \[\leadsto \frac{x}{t - \color{blue}{z \cdot a}} \]

   7. Simplified 72.7%

      \[\leadsto \color{blue}{\frac{x}{t - z \cdot a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+51} \lor \neg \left(z \leq 8 \cdot 10^{+52}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+44} \lor \neg \left(z \leq 1.7 \cdot 10^{-76}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.9e+44) (not (<= z 1.7e-76))) (/ y a) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.9e+44) || !(z <= 1.7e-76)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.9d+44)) .or. (.not. (z <= 1.7d-76))) then
        tmp = y / a
    else
        tmp = x / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.9e+44) || !(z <= 1.7e-76)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.9e+44) or not (z <= 1.7e-76):
		tmp = y / a
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.9e+44) || !(z <= 1.7e-76))
		tmp = Float64(y / a);
	else
		tmp = Float64(x / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.9e+44) || ~((z <= 1.7e-76)))
		tmp = y / a;
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.9e+44], N[Not[LessEqual[z, 1.7e-76]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.9000000000000002e44 or 1.7e-76 < z

   1. Initial program 67.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 67.8%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 67.8%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 50.5%

      \[\leadsto \color{blue}{\frac{y}{a}} \]

   if -2.9000000000000002e44 < z < 1.7e-76

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 62.1%

      \[\leadsto \color{blue}{\frac{x}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+44} \lor \neg \left(z \leq 1.7 \cdot 10^{-76}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 35.5% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \frac{x}{t} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (/ x t))

C

double code(double x, double y, double z, double t, double a) {
	return x / t;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x / t
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x / t;
}

Python

def code(x, y, z, t, a):
	return x / t

Julia

function code(x, y, z, t, a)
	return Float64(x / t)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x / t;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x / t), $MachinePrecision]

Derivation

1. Initial program 84.6%

   \[\frac{x - y \cdot z}{t - a \cdot z} \]
2. Step-by-step derivation

   1. *-commutative 84.6%

      \[\leadsto \frac{x - y \cdot z}{t - \color{blue}{z \cdot a}} \]

3. Simplified 84.6%

   \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
4. Add Preprocessing

5. Taylor expanded in z around 0 38.1%

   \[\leadsto \color{blue}{\frac{x}{t}} \]

6. Final simplification 38.1%

   \[\leadsto \frac{x}{t} \]
7. Add Preprocessing

Developer target: 97.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - a \cdot z\\ t_2 := \frac{x}{t\_1} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{if}\;z < -32113435955957344:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z < 3.5139522372978296 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* a z))) (t_2 (- (/ x t_1) (/ y (- (/ t z) a)))))
   (if (< z -32113435955957344.0)
     t_2
     (if (< z 3.5139522372978296e-86) (* (- x (* y z)) (/ 1.0 t_1)) t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a * z);
	double t_2 = (x / t_1) - (y / ((t / z) - a));
	double tmp;
	if (z < -32113435955957344.0) {
		tmp = t_2;
	} else if (z < 3.5139522372978296e-86) {
		tmp = (x - (y * z)) * (1.0 / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t - (a * z)
    t_2 = (x / t_1) - (y / ((t / z) - a))
    if (z < (-32113435955957344.0d0)) then
        tmp = t_2
    else if (z < 3.5139522372978296d-86) then
        tmp = (x - (y * z)) * (1.0d0 / t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a * z);
	double t_2 = (x / t_1) - (y / ((t / z) - a));
	double tmp;
	if (z < -32113435955957344.0) {
		tmp = t_2;
	} else if (z < 3.5139522372978296e-86) {
		tmp = (x - (y * z)) * (1.0 / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (a * z)
	t_2 = (x / t_1) - (y / ((t / z) - a))
	tmp = 0
	if z < -32113435955957344.0:
		tmp = t_2
	elif z < 3.5139522372978296e-86:
		tmp = (x - (y * z)) * (1.0 / t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(a * z))
	t_2 = Float64(Float64(x / t_1) - Float64(y / Float64(Float64(t / z) - a)))
	tmp = 0.0
	if (z < -32113435955957344.0)
		tmp = t_2;
	elseif (z < 3.5139522372978296e-86)
		tmp = Float64(Float64(x - Float64(y * z)) * Float64(1.0 / t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (a * z);
	t_2 = (x / t_1) - (y / ((t / z) - a));
	tmp = 0.0;
	if (z < -32113435955957344.0)
		tmp = t_2;
	elseif (z < 3.5139522372978296e-86)
		tmp = (x - (y * z)) * (1.0 / t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(a * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / t$95$1), $MachinePrecision] - N[(y / N[(N[(t / z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -32113435955957344.0], t$95$2, If[Less[z, 3.5139522372978296e-86], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024040 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

  :herbie-target
  (if (< z -32113435955957344.0) (- (/ x (- t (* a z))) (/ y (- (/ t z) a))) (if (< z 3.5139522372978296e-86) (* (- x (* y z)) (/ 1.0 (- t (* a z)))) (- (/ x (- t (* a z))) (/ y (- (/ t z) a)))))

  (/ (- x (* y z)) (- t (* a z))))